Mixing-suppressed inelastic dark matter: a minimal model for the LZ 248 keV event

Abstract: We construct a minimal Majorana singlet-vector-like-doublet model for the single nuclear-recoil-like event reported by LZ near 248 keV. At the splitting inferred from the recoil energy, an electroweak-strength $Z$ transition predicts thousands of events; singlet-doublet mixing suppresses the rate without moving the recoil spectrum. Fixed-coupling interpretations instead require a larger splitting in the extreme halo tail, but solar gravitational acceleration removes this suppression, while the larger splitting shifts recoils toward LZ's empty high-energy sideband. In our model the same mixing suppresses solar capture and annihilation, while the small mass gap required for coannihilation weakens Higgs-mediated cooling, allowing the captured population to remain extended and out of equilibrium. Imposing the relic abundance and normalizing the rate to one event leaves a two-dimensional mass-splitting parameter space. A thermalized population gives the conservative IceCube limit $δ=$300-301 keV; with our nonthermal cooling ansatz and elastic scattering treated at tree level, the nominal limit is $δ=$331-341 keV near the 730-733 GeV relic-density endpoint, which is also favored by the recoil spectrum. We outline a gauged $U(1)_N$ origin for the parity and splitting and a candidate $R$-symmetric supersymmetric embedding.